There exists the possibility of directly verifying the theoretical prediction of the existence of excited states of the nucleons at about 45 Mev above the ground state by an inelastic photoelectric dissociation process of the deuteron with γ-rays of energies larger than the excitation energy of these states. The cross section σ′ for such processes is calculated in terms of the elastic cross section σ by using the simplest form of the strong coupling theory. The quantity σ′/σ has a maximum at about 87 Mev where it reaches the approximate value of 0.07. These processes should be experimentally detectable and would furnish valuable information about the properties of nuclei.